This is a minor point, but since Michael Hong brought [into discussion the notation](https://forum.azimuthproject.org/discussion/comment/18388/#Comment_18388), I think the definition:

> for every two objects \$$x,y\$$, one specifies an element \$$\mathcal{X}(x,y)\$$ of \$$\mathcal{V}\$$.

should say "an element \$$\mathcal{X}(x,y)\$$ of \$$V\$$" rather than "[...] of \$$\mathcal{V}\$$" (which denotes a tuple, not a set).